{"id":340,"date":"2025-11-26T15:41:25","date_gmt":"2025-11-26T14:41:25","guid":{"rendered":"https:\/\/web.umons.ac.be\/mapa\/?page_id=340"},"modified":"2025-11-26T15:46:15","modified_gmt":"2025-11-26T14:46:15","slug":"slaag25","status":"publish","type":"page","link":"https:\/\/web.umons.ac.be\/mapa\/slaag25\/","title":{"rendered":"S\u00e9minaire 25"},"content":{"rendered":"<div class=\"x_elementToProof\">\n<div style=\"text-align: center;\"><span style=\"font-size: 18pt; font-family: helvetica, arial, sans-serif;\"><em><strong>Slaag!<\/strong><\/em><\/span><\/div>\n<div class=\"x_elementToProof\">\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt;\"><strong>S\u00e9minaire <\/strong><strong>de Logique, Alg\u00e8bre, Arithm\u00e9tique et G\u00e9om\u00e9trie<\/strong><\/span><\/p>\n<hr \/>\n<\/div>\n<\/div>\n<div><\/div>\n<p><a href=\"https:\/\/web.umons.ac.be\/mapa\/slaag\/\">Page principale du s\u00e9minaire<\/a><\/p>\n<h3>S\u00e9ances de l&rsquo;ann\u00e9e 2025<\/h3>\n<p>&nbsp;<\/p>\n<div>\n<ul>\n<li class=\"x_elementToProof\">\n<div><b><span style=\"color: #004c93;\">Le mercredi 30 avril 2025<\/span> (B\u00e2timent De Vinci, 1er Etage, salle Mirzakhani) <\/b>&#8211; Apr\u00e8s-midi.<\/div>\n<\/li>\n<\/ul>\n<p><strong>13h30-14h30: Vincent Bagayoko (Paris)<\/strong>, Taylor expansions over generalised power series<em><br \/>\n<\/em>R\u00e9sum\u00e9:<em><br \/>\n<\/em>In real or complex analysis, the Taylor expansion of a function at a given point contains all the local information of that function around that point, and Taylor series can be used both to study and to define analytic functions. In o-minimal geometry, it is usual to embed algebras of real-valued regular functions into algebras of functions defined on ordered fields of generalised power series, such as transseries or generalisations thereof. The Taylor expandableness of o-minimal real-valued functions should translate into the existence of formal Taylor expansions of their formal avatars.<br \/>\nI will show how to define Taylor expansions for functions over generalised power series, and show that composition laws on fields of generalised transseries can be understood and defined using such expansions. We will also see that Taylor expansions give an instance of the Lie-type correspondence between derivations and automorphisms on algebras of generalised power series, as described with Krapp, Kuhlmann, Panazzolo and Serra. This is based on joint work with Vincenzo Mantova.<\/p>\n<p><strong>14h50-15h50: Elliot Kaplan (Bonn)<\/strong>,\u00a0Generic derivations on o-minimal structures<br \/>\nR\u00e9sum\u00e9:<br \/>\n<span data-olk-copy-source=\"MessageBody\">Let T be a model complete o-minimal theory that extends the theory of real closed ordered fields (RCF). We introduce T-derivations: derivations on models of T which cooperate with T-definable functions. The theory of models of T expanded by a T-derivation has a model completion in which the derivation acts \u00ab\u00a0generically.\u00a0\u00bb If T=RCF, then this model completion is the theory of closed ordered di\ufb00erential fields (CODF) as introduced by Singer. We can recover many of the known facts about CODF (open core, distality) in our setting. Time permitting, I will also discuss some more recent work on this theory (thorn-rank, Kolchin polynomials). This is joint work with Antongiulio Fornasiero.<\/span><strong><br \/>\n<\/strong><\/p>\n<p><strong>16h10-17h10: Mathias Stout (Leuven)<\/strong>,\u00a0Integration in Hensel minimal fields<br \/>\nR\u00e9sum\u00e9:<br \/>\nAn important theme in the model theory of valued fields is reducing questions about a valued field to ones about its residue field and value group. Model-theoretic frameworks for motivic integration such as the ones developed by Cluckers-Loeser and Hrushovski-Kazhdan achieve a similar reduction on the level of integrals. Such results require a certain tameness of the first order structure under consideration. For example, Hrushovski and Kazhdan work with V-minimal fields.<\/p>\n<div>I will rather consider the more general framework of Hensel minimality, a relatively recent tameness notion introduced by Cluckers, Halupczok and Rideau-Kikuchi. After recalling its basic properties, I will explain how to construct a Hrushovski-Kazdhan style integral for Hensel minimal fields. This includes a version \u00ab\u00a0without\u00a0\u00bb measures, characterizing the definable sets up to definable bijection in the valued field in terms of those in the residue field and value group.<\/div>\n<div>This is joint work with Floris Vermeulen.<\/div>\n<div><\/div>\n<div><\/div>\n<div>\n<hr \/>\n<\/div>\n<ul>\n<li class=\"x_elementToProof\"><b><span style=\"color: #004c93;\">Le mardi 6 mai 2025<\/span> (Pentagone, salle 0A11)<\/b><\/li>\n<\/ul>\n<p><strong>15h45: Valentin Ramlot<\/strong>, On finite subgroups of semisimple algebras &#8211; Introduction<br \/>\nR\u00e9sum\u00e9:<br \/>\nThe structure of semisimple algebras is well-known and is characterized by their Wedderburn decomposition. The finite multiplicative subgroups of such algebras are diverse. We begin a classification of such subgroups up to isomorphism assuming that they are abelian, and therefore products of cyclic groups. We mainly use standard tools coming from field theory and linear algebra.<\/p>\n<p><strong>17h00: Gabriel Ng<\/strong>, <span data-olk-copy-source=\"MessageBody\">A brief introduction to differentially large fields<br \/>\nR\u00e9sum\u00e9:<br \/>\n<\/span><span data-olk-copy-source=\"MessageBody\">Differentially large fields are an analogue for large fields in the context of differential algebra, introduced by Le<\/span><span lang=\"en-US\">on Sanchez and Tressl<\/span>. These are large fields which are equipped with a derivation which is in some sense \u201cgeneric\u201d. Many model-theoretically interesting differential fields are examples of these objects, for instance, differentially closed fields and closed ordered differential fields. In this talk, we will give a gentle introduction to the topic, introducing the necessary concepts and providing motivating examples as necessary.<\/p>\n<hr \/>\n<ul>\n<li class=\"x_elementToProof\"><b><span style=\"color: #004c93;\">Le mercredi 14 mai 2025<\/span> (Pentagone, salle 0A11) <\/b>&#8211; suite des expos\u00e9s de la s\u00e9ance pr\u00e9c\u00e9dente.<\/li>\n<\/ul>\n<p><strong>13h30: Valentin Ramlot<\/strong>, On finite subgroups of semisimple algebras<\/p>\n<p><strong>14h45: Gabriel Ng<\/strong>, Abstract Taylor Morphisms<br \/>\n<span data-olk-copy-source=\"MessageBody\">R\u00e9sum\u00e9:<br \/>\nThe Taylor morphism is a natural construction which generalises the notion of Taylor series from analysis to the algebraic context. In essence, the Taylor morphism turns ring homomorphisms into differential ring homomorphisms into the ring of formal power series. In studying differentially large fields, Leon Sanchez and Tressl introduce a \u201ctwisted\u201d Taylor morphism, which allows us to introduce derivations in the target field. We introduce a generalisation of this notion, and show that all such abstract Taylor morphisms (over fields of arbitrary characteristic) must have a certain concrete form.<\/span><\/p>\n<hr \/>\n<ul>\n<li><b><span style=\"color: #004c93;\">Le mercredi 27 ao\u00fbt 2025<\/span> (B\u00e2timent De Vinci, 1er Etage, salle Mirzakhani) <\/b> &#8211; Journ\u00e9e estivale<\/li>\n<\/ul>\n<div class=\"x_elementToProof\"><\/div>\n<div>\n<div>\n<p>Matin\u00e9e: Pr\u00e9sentation des stages d&rsquo;initiation \u00e0 la recherche (r\u00e9alis\u00e9s \u00e0 l&rsquo;issue du bachelier)<\/p>\n<p><strong>10h-11h: Vanille Zilmia<\/strong>, La th\u00e9orie des corps valu\u00e9s alg\u00e9briquement clos<br \/>\n<strong>11h15-12h15: Chelsea Brohet<\/strong>, Sur la classification des groupes simples : le th\u00e9or\u00e8me de Burnside<\/p>\n<p><strong>12h30-13h30:<\/strong> Lunch, au restaurant universitaire, b\u00e2timent 9<\/p>\n<p>Apr\u00e8s-midi: Expos\u00e9s par des chercheurs<\/p>\n<p><strong>14h00-15h00: Justin Vast (Louvain-la-Neuve)<\/strong>, Groupes BMW, automates, fractales<br \/>\nR\u00e9sum\u00e9:<br \/>\nSoient T et T&rsquo;, deux arbres r\u00e9guliers de degr\u00e9s finis.<br \/>\nUn groupe BMW est un sous-groupe \u0393 \u2a7d Aut(T) x Aut(T&rsquo;) agissant librement et transitivement sur les sommets du produit cart\u00e9sien TxT&rsquo;.<br \/>\nUn groupe BMW \u0393 est dit r\u00e9ductible s&rsquo;il existe un sous-groupe d&rsquo;indice fini de la forme F x F&rsquo; \u2a7d \u0393 , o\u00f9 F \u2a7d Aut(T) et F&rsquo; \u2a7d Aut(T&rsquo;) sont des groupes libres.<br \/>\nUne fa\u00e7on d&rsquo;identifier un groupe BMW irr\u00e9ductible est d&rsquo;y montrer l&rsquo;existence d&rsquo;un anti-tore.<\/p>\n<p>\u00c0 un groupe BMW peut \u00eatre associ\u00e9 un automate de Mealey bireversible.<br \/>\nComme nous le verrons, il est partiellement possible de transf\u00e9rer la notion d&rsquo;anti-tore aux automates de Mealy g\u00e9n\u00e9raux.<br \/>\nUn c\u00e9l\u00e8bre automate de Mayley est celui associ\u00e9 au groupe d&rsquo;allumeur de r\u00e9verb\u00e8res et un \u00ab\u00a0anti-tore\u00a0\u00bb bien choisi de l&rsquo;automate laisse appara\u00eetre le fameux triangle de Sierpi\u0144ski.<\/p>\n<p>Certains anti-tores de groupes BMW irr\u00e9ductibles mettent en \u00e9vidence d&rsquo;autres fractales pour le moins surprenantes&#8230;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div><strong>15h15-16h15: Nicolas Daans (Leuven)<\/strong>, <span data-olk-copy-source=\"MessageBody\">Approaches to undecidability of equations in field theory<\/span><\/div>\n<div>\n<p>R\u00e9sum\u00e9:<br \/>\nIn 1900, David Hilbert poses a question at an international mathematics conference in Paris: Is there an algorithm that can determine whether a given polynomial equation with integer coefficients has an integer solution? The question became known as Hilbert\u2019s 10th Problem. Several decades later, it became increasingly clear that such an algorithm may never exist. This marked the start of a research area on the intersection of logic, algebra, and number theory: to determine which classes of problems from number theory, algebra and geometry are decidable (i.e. solvable by an algorithm) and which are undecidable.<\/p>\n<p>In this talk, I will give a gentle introduction to some of the algebraic and arithmetic ideas underlying approaches to variations of Hilbert&rsquo;s 10th Problem in number theory and field theory. I will in particular give an own interpretation of some ideas of Julia Robinson to study number fields, and of Jan Denef to study function fields. Both Robinson&rsquo;s and Denef&rsquo;s approaches relied, in some way, on the theory of quadratic forms over fields.<\/p>\n<p>Insofar time allows, I will talk about how recent developments on solvability of equations over function fields (like local-global principles for rational points on varieties) can be applied to obtain new results on definability and decidability of equations over function fields of curves. This part will discuss some results of joint research with Karim Johannes Becher and Philip Dittmann, as well as open questions for the future.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div><strong>16h30-17h30: Martin Debaisieux<\/strong>, The Tate module of a height one tamely ramified p-adic dynamical system<\/div>\n<\/div>\n<div>R\u00e9sum\u00e9:<\/div>\n<div>\n<div data-olk-copy-source=\"MessageBody\">Pairs of analytic transformations of some p-adic open unit disk with a fixed point at 0 that commute under composition were studied by Lubin in 1994 under the name of p-adic dynamical systems. He noticed that \u201cfor an invertible series to commute with a noninvertible series, there must be a formal group somehow in the background\u201d. This observation was clarified in subsequent years and led to Lubin&rsquo;s conjecture. Despite the efforts of several mathematicians, this conjecture remains largely open to this day.<\/div>\n<\/div>\n<div><\/div>\n<div>\n<div>I will show how one can turn the set of consistent sequences attached to a mixed commuting pair (f, u) of power series into a crystalline integral p-adic Galois representation of Hodge-Tate weight 1 for which f and u are endomorphisms, in the case of height one over some tame extensions of Qp. This solves the related case of Lubin\u2019s conjecture up to an isomorphism.<\/div>\n<\/div>\n<hr \/>\n<ul>\n<li><strong><span style=\"color: #004c93;\">Le vendredi 17 octobre 2025 apr\u00e8s-midi<\/span> (B\u00e2timent BSM, salle Kohn)<\/strong><\/li>\n<\/ul>\n<p>Kohn room is in the new BSM building (<a href=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/10\/2017\/10\/UMONS_Plan-du-campus-de-la-plaine-de-Nimy2019.pdf\">between building 4 and Avenue du champ de mars<\/a>).<\/p>\n<p><strong>13h30: Wilhelm Klingenberg (Durham)<\/strong>, Holomorphic points of functions, umbilic points of surfaces, and back<br \/>\nR\u00e9sum\u00e9:<br \/>\nWe review what it means for a continuous function of a complex variable to be holomorphic at one point. Then we move to the notion of an umbilic points of a surface in Euclidean space. We finally use a relationship between these to count such points on convex surfaces.<\/p>\n<hr \/>\n<ul>\n<li><strong><span style=\"color: #004c93;\">Le vendredi 14 novembre 2025 \u00e0 partir de 10h30<\/span> (B\u00e2timent BSM, salle Kwolek)<\/strong><\/li>\n<\/ul>\n<p>Kwolek room is in the new BSM building (<a href=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/10\/2017\/10\/UMONS_Plan-du-campus-de-la-plaine-de-Nimy2019.pdf\">between building 4 and Avenue du champ de mars<\/a>).<\/p>\n<p><strong>10h30-11h30: Oussama Bensaid (Louvain)<\/strong>, Quasi-isometric embeddings of right-angled Artin groups<br \/>\nR\u00e9sum\u00e9:<br \/>\nRight-angled Artin groups (RAAGs) are groups defined from a simplicial graph by taking one generator for each vertex and imposing that two generators commute exactly when the corresponding vertices are joined by an edge. They form a rich class of groups interpolating between free groups and free abelian groups. A central theme in geometric group theory, going back to Gromov, is to understand groups up to quasi-isometry. In the case of RAAGs, quasi-isometries are known to display strong rigidity: for many RAAGs, quasi-isometric groups are in fact isomorphic. By contrast, quasi-isometric embeddings between RAAGs are much less understood. In a joint work with Shaked Bader and Harry Petyt, we show that, in many cases, the existence of a quasi-isometric embedding between two RAAGs imposes explicit combinatorial constraints on their defining graphs. I will begin by recalling the definitions and the relevant quasi-isometric background, then describe the new embedding results.<\/p>\n<p><strong>13h30-14h30: Frodo Moonen (Leuven)<\/strong>, <span data-olk-copy-source=\"MessageBody\">Grothendieck Rings of Ordered Subgroups of the Rationals<br \/>\nR\u00e9sum\u00e9:<br \/>\n<\/span>The Grothendieck ring of a first\u2010order structure can be seen as a generalization of the Grothendieck ring of algebraic varieties. This model\u2010theoretic Grothendieck ring serves as a kind of generalized Euler characteristic for definable sets. It encodes interesting combinatorial and geometric information of definable subsets in a structure.<\/p>\n<p>Under the supervision of professor Raf Cluckers and doctor Neer Bhardwaj, I explored the Grothendieck rings of subgroups of Q in the language of ordered abelian groups. While the edge cases were already known \u2013 trivial for (Z ; +, &lt;) and isomorphic to Z[T ]\/(T^2 + T ) for (Q ; +, &lt;) &#8211; no research had been done on the intermediate groups. My master\u2019s thesis aimed to fill this gap. In this talk, I will present the results and share some of the key ideas behind the proofs.<\/p>\n<p><strong>14h45-15h45: Giovanni Bosco<\/strong>, Tate modules of Abelian varieties with wild potential good reduction<br \/>\nR\u00e9sum\u00e9:<br \/>\nAbelian varieties over Qp give rise to p-adic representations of G_{Qp} via their associated Tate modules. We are interested in the inverse problem, that is, to determine when such a representation arises from an Abelian variety over Qp. M. Volkov has given an answer in the case of elliptic curves for p \u2265 5 and Abelian varieties with tame potential good reduction. In this talk we will discuss the case of wild potential good reduction. We will present a full classification of the 3-adic representations arising from elliptic curves over Q_3 with potential good reduction. Then, we will discuss the case of surfaces over Qp for p= 3,5.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Slaag! S\u00e9minaire de Logique, Alg\u00e8bre, Arithm\u00e9tique et G\u00e9om\u00e9trie Page principale du s\u00e9minaire S\u00e9ances de l&rsquo;ann\u00e9e 2025 &nbsp; Le mercredi 30 avril 2025 (B\u00e2timent De Vinci, 1er Etage, salle Mirzakhani) &#8211; Apr\u00e8s-midi. 13h30-14h30: Vincent Bagayoko (Paris), Taylor expansions over generalised power series R\u00e9sum\u00e9: In real or complex analysis, the Taylor expansion of a function at a [&hellip;]<\/p>\n","protected":false},"author":297,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-340","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>S\u00e9minaire 25 - Service \/ FS - Math\u00e9matiques appliqu\u00e9es<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/web.umons.ac.be\/mapa\/slaag25\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"S\u00e9minaire 25 - Service \/ FS - Math\u00e9matiques appliqu\u00e9es\" \/>\n<meta property=\"og:description\" content=\"Slaag! 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